Serdica Mathematical Journal

Volume 22, Number 2, 1996

C O N T E N T S

• Adly, S. A perturbed iterative method for a general class of variational inequalities. (pp. 69-82)
• Stamov, G. T. Application of Lyapunov's direct method to the existence of integral manifolds of impulsive differential equations. (pp. 83-90)
• Markov, Y. Limit cycles of perturbations of a class of quadratic Hamiltonian vector fields. (pp. 91-108)
• Tsvetkov, D. P. A periodic Lotka-Volterra system. (pp. 109-116)
• Kravvaritis, D., G. Pantelidis. A random evolution inclusion of subdifferential type in Hilbert spaces. (pp. 117-124)
• Georgiev, V. Existence of global solutions to supercritical semilinear wave equations. (pp. 125-164)

A B S T R A C T S

A PERTURBED ITERATIVE METHOD FOR A GENERAL CLASS OF VARIATIONAL INEQUALITIES
Samir Adly

1991 Mathematics Subject Classification: 47H19, 47H17, 49J40, 65J05.
Key words: Variational inequalities, Wiener-Hopf equation, proximal mapping, variational convergence, Mosco-convergence, co-coercive mapping.

The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.

APPLICATION OF LYAPUNOV'S DIRECT METHOD TO THE EXISTENCE OF INTEGRAL MANIFOLDS OF IMPULSIVE DIFFERENTIAL EQUATIONS
G. T. Stamov

1991 Mathematics Subject Classification: 34A37.
Key words: integral manifold, impulsive differential equations.

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations.
By means of piecewise continuous functions which are generalizations of the classical Lyapunov's functions, sufficient conditions for the existence of integral manifolds of such equations are found.

LIMIT CYCLES OF PERTURBATIONS OF A CLASS OF QUADRATIC HAMILTONIAN VECTOR FIELDS
Yavor Markov

1991 Mathematics Subject Classification: 58F21, 34C05.
Key words: Limit cycles, Abelian integrals, Picard-Lefschetz formula.

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

A PERIODIC LOTKA-VOLTERAa SYSTEM
D. P. Tsvetkov

1991 Mathematics Subject Classification: 34A25, 92B20.
Key words: 34A25, 92B20}{periodic Lotka-Volterra system Predator-Prey.

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.

A RANDOM EVOLUTION INCLUSION OF SUBDIFFERENTIAL TYPE IN HILBERT SPACES
D. Kravvaritis, G. Pantelidis

1991 Mathematics Subject Classification: 47H06, 47H15.
Key words: subdifferential, evolution inclusions, Hausdorff continuity, measurable multifunctions.

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

EXISTENCE OF GLOBAL SOLUTIONS TO SUPERCRITICAL SEMILINEAR WAVE EQUATIONS
V. Georgiev

1991 Mathematics Subject Classification: 35L05, 35L70, 35B40.
Key words: semilinear wave equation, Strichartz estimate.